Recording a Video Mix

Depends on what operative system you use I guess.
On mac you can use quick time to record the video with sound without too much difficulty.
A more expensive software is Wirecast (which mainly used for streaming audio/video) that has option to save to file.
I personally dont record anything, I let the video streaming site that I’m using (http://vjstream.tv) record everything for me and I can either publish it there or download it.